In triangle ABC, if #a = 8.75# centimeters, #c = 4.26# centimeters, and #m/_B# is #87°# what is the length of #b# to two decimal places?

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Answer 1 · 2018-08-13T07:07:42

#:.b~~9.53 " cm"#

We know that ,

#color(red)("cosine Rule : " cosB=(c^2+a^2-b^2)/(2ca))#

#:.2cacosB=c^2+a^2-b^2#

#:.b^2=c^2+a^2-2cacosB...to(1)#

We have ,

#a=8.75" cm" ,# , #c=4.26 " cm" and B=87^circ#

Using #(1)# we get

#b^2=(4.26)^2+(8.75)^2-2(4.26)(8.75)cos87^circ#

#:.b^2=18.1476+76.5625-74.55(0.0523)#

#:.b^2~~90.81135#

#:.b~~9.529# cm